Region is bounded by the parabola and the vertical line .
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
Region R is bounded by the parabola x=y2 and the vertical line x=4.
(1) Sketch or describe the graph of R, clearly indicating all intersection points with their coordinates.
(2) Determine whether calculating the area of R by integrating with respect to x or with respect to y requires fewer definite integrals. Justify your answer based solely on geometric considerations of the region.
(3) Write, but do not evaluate, a single definite integral that represents the area of R using the variable you identified in part (b).